LSU College of Science
LSU  | Mathematics

Math 1022 Trigonometry Topics

An Introduction to Angles: Degree and Radian Measure

  • Understanding degree measure and radian measure
  • Converting between degree measure and radian measure
  • Finding coterminal angles using degree measure and radian measure

Applications of Radian Measure

  • Determining the area of a sector of a circle
  • Determining the arc length of a sector of a circle

Triangles (Review)

  • Classifying triangles
  • Using the Pythagorean Theorem
  • Understanding similar triangles
  • Understanding the special right triangles

Right Triangle Trigonometry

  • Understanding the right triangle definitions of the trigonometric functions
  • Using the special right triangles
  • Understanding the fundamental trigonometric identities
  • Understanding cofunctions
  • Evaluating trigonometric functions using a calculator

Trigonometric Functions of General Angles

  • Understanding the four families of special angles
  • Understanding the definitions of the trigonometric functions of general angles
  • Finding the values of the trigonometric functions of quadrantal angles
  • Understanding the signs of the trigonometric functions
  • Determining reference angles
  • Evaluating trigonometric functions ofangles belonging to the $\frac{\pi}{3}$, $\frac{\pi}{4}$, and $\frac{\pi}{6}$ families

The Unit Circle

  • Understanding the definition of the unit circle
  • Understanding the unit circle definitions of the trigonometric functions

The Graphs of the Trigonometric Functions

  • Understanding the graphs of the sine, cosine, tangent, cotangent, secant, and cosecant functions and their properties
  • Sketching graphs of the form y=Asin(Bx-C)+D or y=Acos(Bx-C)+D
  • Sketching graphs of the form y=Atan(Bx-C)+D or y=Acot(Bx-C)+D
  • Sketching graphs of the form y=Asec(Bx-C)+D or y=Acsc(Bx-C)+D
  • Determine the equation of a function of the form y=Asin(Bx-C) or y=Acos(Bx-C) given its graph

Inverse Trigonometric Functions

  • Understanding and finding the exact and approximate values of the inverse sine function, the inverse cosine function, and the inverse tangent function
  • Evaluating composite functions involving inverse trigonometric functions of the forms $f∘f^{-1}$, $f^{-1}∘f$, $f∘g^{-1}$, and $f^{-1}∘g$

Trigonometric Identities

  • Substituting known identities to verify an identity
  • Changing to sines and cosines to verify an identity
  • Factoring to verify an identity
  • Separating a single quotient into multiple quotients to verify an identity
  • Combining fractional expressions to verify an identity
  • Multiplying by conjugates to verify an identity

The Sum and Difference Formulas

  • Understanding and using the sum and difference formulas for the cosine, sine, and tangent functions
  • Using the sum and difference formulas to verify identities
  • Using the sum and difference formulas to evaluate expressions involving inverse trigonometric functions

The Double-Angle and Half-Angle Formulas

  • Understanding and using the double-angle formulas and the half-angle formulas
  • Using the double-angle and half-angle formulas to verify identities
  • Using the double-angle and half-angle formulas to evaluate expressions involving inverse trigonometric functions

Trigonometric Equations

  • Solving trigonometric equations that are linear or quadratic in form
  • Solving trigonometric equations using identities
  • Solving other types of trigonometric equations
  • Solving trigonometric equations using a calculator

Right Triangle Applications

  • Solving right triangles
  • Solving applications using right triangles

The Law of Sines

  • Determining if the Law of Sines can be used to solve an oblique triangle
  • Using the Law of Sines to solve the SAA case or the ASA case
  • Using the Law of Sines to solve the SSA (Ambiguous) case
  • Using the Law of Sines to solve applied problems involving oblique triangles

The Law of Cosines

  • Determining if the Law of Cosines can be used to solve an oblique triangle
  • Using the Law of Cosines to solve the SAS case
  • Using the Law of Cosines to solve the SSS case
  • Using the Law of Cosines to solve applied problems involving oblique triangles

Area of Triangles

  • Determining the area of oblique triangles
  • Using Heron’s Formula to determine the area of an SSS triangle
  • Solving applied problems involving the area of triangles

Polar Coordinates and Polar Equations

  • Plotting points using polar coordinates
  • Determining different representations of a point (r, θ)
  • Converting points from polar to rectangular coordinates and from rectangular to polar coordinates
  • Converting equations from rectangular to polarform and from polar to rectangular form

Graphing Polar Equations

  • Sketching equations of the form $r\cosθ = a$, $r\sinθ = a$, $ar\cosθ + br\sinθ = c$, and $θ = α$
  • Sketching equations of the form $r = a$, $r = a\sinθ$, and $r = a\cosθ$
  • Sketching equations of the form $r = a + b\sinθ$ and $r = a + b\cosθ$
  • Sketching equations of the form $r = a\sin(nθ)$ and $r = a\cos(nθ)$
  • Sketching equations of the form $r^{2} = a^{2}\sin(2θ)$ and $r^{2} = a^{2}\cos(2θ)$

Vectors

  • Understanding the geometric representation of a vector
  • Understanding operations on vectors represented geometrically
  • Understanding vectors in terms of components
  • Understanding vectors in terms of i and j
  • Finding a unit vector
  • Determining the direction angle of a vector
  • Representing a vector in terms of i and j given its magnitude and direction angle
  • Using vectors to solve applied problems involving velocity